You can't exactly walk into a fine dining establishment off the street and expect to be hired as a sommelier, but you can achieve the title with much less training than for most other occupations. There are plenty of courses available you can attend to become certified, many of them only lasting six months or so.
You also won't rack up a ton of debt, as you can enroll in one of these programs for as little as $800 (although more often they'll be at least a couple grand).
After earning your Certified Sommelier Certificate (redundant much?), you can go after your Advanced Sommelier Certificate, and eventually even your Master Sommelier Diploma.
This coveted credential basically tells people that you might as well have lived your entire life inside of a wine barrel (after age twenty-one of course) for all you know about fine wines. You don't wear a special hat or anything, but people will be quite aware that you know your stuff.